Question

गुणनखंड विधि से निम्न द्विघात समीकरणों के मूल ज्ञात कीजिएः
(i) $x^{2}-3x-10=0$
(ii) $2x^{2}+x-6=0$
(iii) $\ sqrt{2}x^{2}+7x+5\sqrt{2}=0$
(iv) $2x^{2}-x+\frac{1}{8}=0$
(v) $100x^{2}-20x+1=0$

Answer 1

(i) x² - 3x - 10 = 0
या, x² - 5x + 2x - 10 = 0
या, x(x -5) + 2(x - 5) = 0
या, (x + 2)(x - 5) = 0
या, x = -2, 5

(ii) 2x² + x - 6 = 0
या, 2x² + 4x - 3x - 6 = 0
या, 2x(x + 2) -3(x + 2) = 0
या, (2x - 3)(x + 2) = 0
या, x = 3/2 , -2

(iii) √2x² + 7x + 5√2 = 0
या, √2x² + 2x + 5x + 5√2 = 0
या, √2x(x + √2) + 5(x + √2) = 0
या, (√2x + 5)(x + √2) = 0
या, x = -5/√2 , -√2

(iv) 2x² - x + 1/8 = 0
या, 16x² - 8x + 1 = 0
या, 16x² - 4x - 4x + 1 = 0
या, 4x(4x - 1) -(4x - 1) = 0
या, (4x - 1)(4x - 1) = 0
या, x = 1/4 , 1/4


(v) 100x² - 20x + 1 = 0
या, 100x² - 10x - 10x + 1 = 0
या, 10x(10x - 1) - (10x - 1) = 0
या, (10x - 1)(10x - 1) = 0
या, x = 1/10, 1/10